[BlindMath] I need help with vectors and electric field

[Jonathan Fine]

Hi Abdulqadir

A force has a magnitude and a direction. Coulomb's law has two parts. The
first part gives the magnitude of the force. The second part gives the
direction of the force.

In plane Cartesian coordinates we can write the force as a vector. For
example, (1, 0) is a unit force to the x-direction, and (0, 1) is a unit
force in the y-direction.

We can add forces by adding components. So (1,0) + (0,1) = (1, 1).

Now, (1, 1) is a diagonal force, with equal components in the x and y
directions. The magnitude of this force is given by Pythagorus theorem. It
is the square root of the sum of the square of the magnitudes. In this case
it is the square root of 2, which is about 1.414.

Suppose we have charged particles at (0,0) and (1,1) and the charges are
such that Coulomb's law gives a force of magnitude one. What is the
resulting vector, in plane Cartesian coordinates? Well, its direction is on
the diagonal line from (0, 0) to (1, 1). But it is not (1, 1), because that
has magnitude 1.414.

There are two correct answers. The first is approximately (0.707, 0.707).
This has magnitude one. The other is the equal but opposite force (-0.707,
-0.707). It may help to remember that 0.7 squared is 0.49, which is almost
a half.

I hope this helps you find the calculation needed to solve your problem.
Remember that in Physics a force has a magnitude and a direction. The
magnitude of the sum of two forces depends on their magnitudes, and also on
the angle between their directions. The simplest example is 1 + 1 = 2 and 1
- 1 = 0. For 1+ 1 the angle is zero, and for 1 - 1 the angle is 180 degrees.

I hope this helps. For sighted persons I would draw a diagram to engage
with the visual imagination.

with kind regards

Jonathan